HSC Mathematics Extension 1: complete 2026 guide (modules, exam, scaling, strategy)

HSC Mathematics Extension 1 is the 1-unit course that sits on top of Mathematics Advanced. Together they form a 3-unit study and the two papers are sat as separate HSC exams. Extension 1 is taken by students aiming at high ATARs, STEM degrees, or commerce and actuarial pathways.

This page is the index. Below you will find the topic breakdown, exam structure, scaling notes, study strategy, and links to every dot point and deep guide we have.

Two syllabuses are live in 2026

HSC Mathematics Extension 1 is in a syllabus transition.

If you are sitting the HSC in 2026 (currently Year 12), you follow the 2017 syllabus. Topics: Functions, Trigonometric Functions, Calculus, Combinatorics (Year 11 ME-A1), Proof by Induction, Vectors (Year 12 ME-V1), and the Binomial Distribution.

If you are starting Year 11 in 2026 (HSC 2027 onwards), you follow the new 2024 syllabus. Most content is identical, with adjusted emphasis and updated assessment structures. Vectors and projectile motion are unchanged in scope. Statistical inference is slightly expanded.

This hub covers both syllabuses where they differ. Check with your school which syllabus your cohort is on.

The seven topics

Functions (ME-F1, ME-F2)

Polynomial functions, division algorithm, remainder and factor theorems, multiple roots and multiplicity, polynomial inequalities, parametric equations, and graphs of reciprocal and rational functions.

Trigonometric functions (ME-T1, ME-T2, ME-T3)

Inverse trigonometric functions ($\arcsin$, $\arccos$, $\arctan$) including their graphs, domains and ranges. Sum, difference, double and product-to-sum identities. The auxiliary angle technique. General solutions of trigonometric equations and the t-formula (Weierstrass substitution).

Calculus (ME-C1, ME-C2, ME-C3)

Related rates and exponential growth and decay. Integration by substitution, including reverse chain rule cases. Integration giving inverse trigonometric functions. Volumes of revolution. Separable differential equations and their applications. Projectile motion.

Combinatorics and the binomial theorem (ME-A1)

Permutations, combinations, the pigeonhole principle, and the binomial theorem with Pascal's triangle.

Proof by mathematical induction (ME-P1)

Induction on series, divisibility statements, and inequalities. Structuring an induction proof: base case, induction hypothesis, induction step, conclusion.

Vectors (ME-V1)

Two-dimensional vectors, vector arithmetic, magnitude and direction. The scalar (dot) product, the angle between two vectors, and orthogonality. Projection of one vector onto another. Parametric vector equations of lines. Geometric proofs using vectors.

Statistical analysis (ME-S1)

The Bernoulli trial, the binomial distribution, mean and variance of $X \sim B(n, p)$, exact binomial probabilities, and the normal approximation of the binomial.

Exam structure

HSC Mathematics Extension 1 is sat as a single 2-hour paper plus 10 minutes reading time, in addition to the Mathematics Advanced paper.

• Section I: Multiple choice, 10 questions, 10 marks
• Section II: Free response, 14 questions, 60 marks

Total: 70 marks.

The paper covers both Year 11 and Year 12 Extension 1 content. Multi-step extended questions in the back third of Section II combine topics: a typical Q14 might thread vectors through a projectile problem, or combine induction with combinatorics.

Bring a NESA-approved scientific calculator. Graphics calculators are not used in NSW HSC Mathematics.

How Extension 1 scales (2026)

Mathematics Extension 1 typically scales to a mean scaled mark per unit of around 41-43 out of 50. It is consistently the second-highest-scaling HSC subject (behind Mathematics Extension 2) and lifts the overall ATAR aggregate significantly when sat alongside Advanced. For comparison:

• Mathematics Extension 2: scales to around 46-47 per unit (highest most years)
• Mathematics Extension 1: scales to around 41-43 per unit
• Mathematics Advanced: scales to around 34-35 per unit
• Mathematics Standard 2: scales to around 25 per unit

A raw HSC mark of 80 in Extension 1 (a Band E4) typically scales to about 47-48, which is exceptional for ATAR. Try our HSC ATAR calculator to model your projected ATAR from Extension 1 plus your other subjects.

Bands in Extension 1 are labelled E1 to E4 rather than 1 to 6 (because it is a 1-unit course). E4 starts at 80%, E3 at 65%, E2 at 50%. Most strong cohorts aim for E3 or E4.

Study strategy

Extension 1 rewards consistent weekly practice over short, intense cramming sessions. The standard approach is:

1. Master Advanced first. Extension 1 sits on top of Advanced calculus, functions and trig. If you cannot quickly differentiate a chain-rule composite or integrate by substitution, Extension 1 questions will be unforgiving.
2. Build the syllabus into a topic-by-topic checklist. Use the dot point pages on this site as your spine.
3. Drill standard techniques. Induction, integration by substitution, vector dot product, binomial probability and the t-formula are the bread and butter of the paper.
4. Do at least 8 full past papers under timed conditions in the final two terms. Mark them honestly against the NESA marking guidelines.
5. Keep a mistakes book. Note every careless slip and re-do the question a week later.

Our 2026 deep guides

We have written in-depth guides for the high-stakes Extension 1 topics:

• HSC Maths Ext 1 binomial theorem and combinatorics deep dive
• HSC Maths Ext 1 mathematical induction deep dive
• HSC Maths Ext 1 vectors deep dive

Each guide includes worked examples, exam-style questions, and links to the relevant NESA syllabus dot points.

System context

HSC Mathematics Extension 1 sits inside the wider HSC system. Related explainers:

• How the HSC ATAR is calculated covers UAC's aggregate and scaling mechanics.
• How HSC subjects are scaled explains why Extension 1 scales much higher than Advanced or Standard.
• HSC bonus points and EAS covers subject-specific selection-rank bonuses (Mathematics Extension 1 earns bonus points at most NSW engineering, science and actuarial degrees).

How to use this hub

If you are a Year 12 student sitting HSC 2026: work through every Year 12 module dot point on this site, then return to weak Year 11 dot points. Aim for 8 to 12 timed past papers in Term 4.

If you are a Year 11 student on the new 2024 syllabus: read the Year 11 dot points (Functions, Trig, Calculus, Combinatorics) carefully and start banking the Year 12 dot points as your school covers them.

For the official NESA syllabus, prescribed reference material, and past papers, refer to educationstandards.nsw.edu.au.